Many-Body Radiative Decay in Strongly Interacting Rydberg Ensembles

Chris Nill, Kay Brandner, Beatriz Olmos, Federico Carollo, and Igor Lesanovsky

Phys. Rev. Lett. 129, 243202 – Published 9 December 2022

Abstract

When atoms are excited to high-lying Rydberg states they interact strongly with dipolar forces. The resulting state-dependent level shifts allow us to study many-body systems displaying intriguing nonequilibrium phenomena, such as constrained spin systems, and are at the heart of numerous technological applications, e.g., in quantum simulation and computation platforms. Here, we show that these interactions also have a significant impact on dissipative effects caused by the inevitable coupling of Rydberg atoms to the surrounding electromagnetic field. We demonstrate that their presence modifies the frequency of the photons emitted from the Rydberg atoms, making it dependent on the local neighborhood of the emitting atom. Interactions among Rydberg atoms thus turn spontaneous emission into a many-body process which manifests, in a thermodynamically consistent Markovian setting, in the emergence of collective jump operators in the quantum master equation governing the dynamics. We discuss how this collective dissipation—stemming from a mechanism different from the much studied superradiance and subradiance—accelerates decoherence and affects dissipative phase transitions in Rydberg ensembles.

Received 16 June 2022
Accepted 7 November 2022

DOI:https://doi.org/10.1103/PhysRevLett.129.243202

Physics Subject Headings (PhySH)

Open quantum systems & decoherence Phase diagrams Rydberg gases Spontaneous emission

Atomic, Molecular & Optical

Authors & Affiliations

Chris Nill ¹, Kay Brandner ², Beatriz Olmos ^1,2, Federico Carollo ¹, and Igor Lesanovsky ^1,2

¹Institut für Theoretische Physik, Universität Tübingen, Auf der Morgenstelle 14, 72076 Tübingen, Germany
²School of Physics and Astronomy and Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, The University of Nottingham, Nottingham NG7 2RD, United Kingdom

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Vol. 129, Iss. 24 — 9 December 2022

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Images

Figure 1
Rydberg atoms and collective dissipation. (a) One-dimensional lattice gas of interacting atoms resonantly driven by a laser with Rabi frequency $Ω$ . Neighboring atoms interact with interaction strength $V$ when simultaneously excited to their Rydberg state $| ↑ ⟩$ . Rydberg states decay under the emission of a photon to the ground state $| ↓ ⟩$ at rate $γ$ . (b) Decay in a system of two atoms. When the interaction strength $V$ is larger than the natural linewidth $γ$ it is possible to discern whether a decaying Rydberg atom had an excited neighboring atom or not. This information can be inferred from the frequency of the emitted photon: $ν_{1}$ , excited neighboring atom; $ν_{0}$ , neighboring atom in the ground state. (c) Graphical representation of projectors $P_{k}^{ξ}$ which project on the subspace where the neighborhood of a reference atom (empty circle) contains $ξ$ excited atoms (in two dimensions). Because of the strong nearest-neighbor interaction an emitted photon carries information on the subspace from which the emission took place, leading to collective jump operators.
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Figure 2
Bistability region in the mean field phase diagram in the presence of single-atom and collective decay. In the gray region the stationary state of the mean field equations is unique. In the colored region, whose shape depends on the dimension $d$ , two stationary solutions exist. The cusps culminate in critical points, which are marked by crosses. The inset shows a cut of the stationary state density through the bistability region, taken at $Ω = 2.5 γ$ . The red (blue) curves show the stationary Rydberg excitation density $n_{ss}^{c}$ ( $n_{ss}^{s}$ ), where the superscript $c$ ( $s$ ) refers to collective (single-atom) decay of collective (single-atom) decay. Solid and dashed lines mark the two stationary solutions. We have set $d V = 10 γ$ . The mean field equations for $n_{ss}^{c}$ are in Eq. (7) while those for $n_{ss}^{s}$ are given in Ref. [44].
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Figure 3
Stationary state of a $d = 1$ chain with periodic boundaries. Shown is the stationary density of Rydberg excitations as a function of the laser detuning $Δ$ and the Rabi frequency $Ω$ with $V = 10 γ$ in the presence of single-body decay ( $n_{ss}^{s}$ ) and collective many-body decay ( $n_{ss}^{c}$ ). The data are obtained by solving Eq. (5) with Hamiltonian (6). In the rightmost column we show the relative difference between the two densities, $δ n_{ss} = (n_{ss}^{c} - n_{ss}^{s}) / n_{ss}^{s}$ . Significant deviations are visible for negative detunings in the region where bistable behavior is predicted by the mean field analysis. To estimate the steady state we average over 100 linearly spaced data points in the interval $[4.75 γ t, 5.00 γ t]$ . The oscillations visible in the region $Δ / γ > 0$ are a finite time effect. The data for $N = 4$ are obtained by exact diagonalization, while the $N = 8$ data were calculated using continuous-time quantum jump Monte Carlo averaged over 300 trajectories.
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